Surface and surface area

  • Cubes
    problem
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    Cubes

    Age
    7 to 11
    Challenge level
    1 out of 3

    How many faces can you see when you arrange these three cubes in different ways?

  • Brush Loads
    problem
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    Brush Loads

    Age
    7 to 11
    Challenge level
    1 out of 3

    How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

  • Changing areas, changing volumes
    problem
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    Changing Areas, Changing Volumes

    Age
    11 to 14
    Challenge level
    2 out of 3

    How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

  • Cuboids
    problem
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    Cuboids

    Age
    11 to 14
    Challenge level
    3 out of 3

    Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

  • Cola can
    problem
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    Cola Can

    Age
    11 to 14
    Challenge level
    3 out of 3

    An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

  • Three cubes
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    Three Cubes

    Age
    14 to 16
    Challenge level
    2 out of 3

    Can you work out the dimensions of the three cubes?

  • Painted Cube
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    Painted Cube

    Age
    14 to 16
    Challenge level
    2 out of 3

    Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

  • The Spider and the Fly
    problem
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    The Spider and the Fly

    Age
    14 to 16
    Challenge level
    2 out of 3

    A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

  • problem
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    Funnel

    Age
    14 to 16
    Challenge level
    3 out of 3

    A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

  • Four Points on a Cube
    problem

    Four Points on a Cube

    Age
    16 to 18
    Challenge level
    1 out of 3
    What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?